INTERCHANGE OF HEAT VON BEZOLD 383 



be seen from the observations in balloons that R. Assmann will soon 

 publish. 9 



It is very important to devise methods that will enable us to at 

 least approximately measure the reflection from the surfaces of the 

 earth and the clouds. But these are questions that will be fully 

 considered hereafter. At present we are concerned only to obtain 

 a general view as to the most important of the quantities under 

 consideration. This object seems now to have been attained and I 

 will proceed to the closer study of the matter. 



Before I treat closely the individual problems that offer them- 

 selves, I will establish a number of theorems that will serve as guides 

 for all that follows. These theorems are of such simple nature that 

 they might seem almost self-evident and can easily be expressed 

 in words. But I will also put them in the shape of formulas, although 

 these latter become more complex than would be expected from 

 the simple verbal expressions. Nevertheless, I find it expedient to 

 give them such a form. By this means we not only attain accuracy 

 of expression and thus remove every chance of misunderstanding, 

 but we can from the formulas deduce a number of individual items 

 that would otherwise be overlooked. 



(il.) GENERAL THEOREMS 



The next following theorems are all founded on the assumption 

 that we may consider the thermal condition of the earth as a station- 

 ary one, or more correctly, one that is periodically stationary. 



These therefore assume that there are average values of all the 

 quantities considered which remain the same within small limits 

 of error when we have deduced them from a sufficiently long series 

 of years of observation without regard to the exact length of the 

 series or to the year with which it began. 



These theorems depend upon the justifiable assumption that the 

 earth, at least within the time covered by our observations, has 

 neither become warmer nor colder and that the succession of 

 seasons goes on as uniformly as ever at every point on the earth's 

 surface. 



Hence, all the quantities that we consider except the times, the 

 dimensions, the coordinates, etc. , represent average values as obtained 

 from series of observations that are long enough to allow of apply- 

 ing to them the fundamental laws of averages, and yet not so long 



9 R. Assmann and A. Berson: Wissenschaftliche Luftfahrten. Volumes 

 II and III. Braunschweig, 1900. 



